We have two rabbits since a year now. Originally a boy/girl sibling pair but the boy died unfortunately from a throat issue (couldn't eat anymore) and so we got the girl a new friend.
All came from an animal rescue, they are normally checked by a vet, come fully vaccinated and should also be neutered, both male and female. I had non-neutered females before and had fake pregnancies which stressed both girls and also both died from uterine cancer. There are so many abandoned rabbits, getting them from a rescue means unloved animals are having a great second chance. Most of them don't end there because of behaviour issues but because the owner got bored or couldn't cope for various reasons.
Both live outside in a hutch/run combo plus they have a 10ft run on the lawn. They live outside the whole year so in winter they are buried in a mountain of straw plus the hutch is covered in insulation foil and tarpaulin.
My two don't like to be picked up. My friend's rabbit is the most placid one you can find, he is not bothered at all. So, it really depends on the individual animal. But even if they are just for stroking in the run they are very funny, have great personalities and entertaining.
They need stuff to chew on. Rabbit teeth grow so hard things like cardboard boxes/tubes, willow tubes and balls etc are necessary on a daily basis. The hay also takes care of it but it is not really enough.